Some thoughts, as you are contemplating a type of setup that is not terribly difficult (millions have done it) but does require some knowledge.
Typically, some form of software is used to control playback between a server or share with music files (your PC) and a network-connected renderer (the Matrix). The control software is usually run on a phone or tablet, though sometimes, it can be run on a PC. Matrix provides its mConnect software, which I've not used, but you could see if a manual is downloadable.
The classic and serviceable version of this is a DLNA server running on the PC (or NAS), a control point running on a phone, and the renderer (Matrix).
One issue is that in the dedicated LAN you propose to set up -- or in any LAN -- each device must be assigned a unique IP address. Does your switch include a DHCP server to do that?
I hope that's helpful.